Statistics and Data Analysis
Instance: 2020/2021 - 2S
Cycles of Study/Courses
Teaching Staff - Responsibilities
Teaching - Hours
|Theoretical and practical :
Train students in multivariate data analysis methods in order to extract essential information from a potentially voluminous set of data with a focus on supervised and unsupervised learning methods.
Learning outcomes and competences
1. Understanding the theoretical foundations of the methodologies taught.
2. Ability to extract essential information from a set of real data, using the methodologies taught
And in particular:
- Recognize different problems of unsupervised classification and supervised classification and solve them using the methods addressed and using software R;
- Prepare, solve and present computational data mining projects, where the various models presented are discussed, evaluated and compared in concrete cases.
- Solve computational and non-computational exercises on the methodologies addressed
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Previous knowledge on random variables, probability distribution, sample statistics, confidence intervals and hypothesis tests is required. Those are usual contents of an introductory course on Probability and Statistics for undergrduate students.
1 Brief summary of random vectors. Multivariate normal distribution.
Selection of Linear Models and Regularization (Ridge and Lasso Regression). Bias-variance tradeoff.
Feature screening for ultrahigh dimensional predictors.
Clustering: Partition methods, hierarchical methods, probabilistic method and model based clustering.
Statistical decision theory. Bayes rules of minimum error and minimum cost.
Linear and quadratic discriminant analysis.
Nonparametric estimation of probability density functions: kernel and the kth nearest neighbor methods.
Factorial Analysis: Principal Component Analysis, Simple and Multiple Correspondence Analysis.
apontamentos escritos disponibilizados pelos professores
James Gareth 070; An introduction to statistical learning
. ISBN: 978-1-4614-7137-0
Everitt Brian S.; Applied multivariate data analysis. ISBN: 978-0-470-71117-0
. ISBN: 0-387-95284-5
. ISBN: 978-0-521-86116-8
Sharma, Subhash; Applied multivariate techniques. ISBN: 0-471-31064-6
Hair Jr Joseph F.; Multivariate data analysis. ISBN: 0-13-515309-3
Jianqing Fan and Runze Li and Cun-Hui Zhang ; Statistical Foundation of Data Science , Chapman and Hall/CRC; 1 edition, 2019. ISBN: 978-1466510845
Teaching methods and learning activities
Classes will be simultaneously theoretical and practical, with several examples of application and always making use of statistical software. The used software will be SPSS or the free programming language R (depending on the masters course).
Physical sciences > Mathematics > Statistics
Distributed evaluation without final exam
Amount of time allocated to each course unit
|Frequência das aulas
Eligibility for exams
Attendency is not mandatory. The computational project, which must be presented by the students, is mandatory.
Calculation formula of final grade
1. Evaluation will be distributed without a final examination. There is however an exam in the second evaluation period (“época de recurso”).
2. Exam in the second evaluation period (“época de recurso”): students who have failed in the tests and project (final mark less than 9.5) can take an exam in the second evaluation period (“época de recurso”) and take one or both parts. For each part, the final score is the maximum of the marks obtained by test and exam. The mark obtained in the written assignment/project cannot be improved in any evaluation period.
The subject is divided into two parts. Each part consists of a practical work and a test / exam. For each student the marks of the works and tests are given by:
Scores_of_works: max (2/3*work1 +1/3*work2, 1/2*work1+1/2*work2)
Scores_of_tests: max (2/3*Test1 +1/3*Test2, 1/2*Test1+1/2*Test2)
Final Score: 0.6* Scores_of_tests+0.4*Scores_of_works. The same procedure applies in the case of the two parts of the exam.
Approval is subject to the value of Score_of_tests (or both parts of the exam), calculated by the above formula, being equal to or higher than 7.0 values (on a scale of 0 to 20).
The practical works consist of the analysis of a real database, using the methods taught, using software.
It should be done by groups of 2 students.
Improvement of the final mark: students that have succeed and attend the exam (“época de recurso”) in order to improve their final mark, have to take both parts. The mark obtained in the written assignment/project cannot be improved in any evaluation period. The evaluation formula is the same (see above).